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171.

An infinite number of charges, each equal to q, are placed along the x-axis at x=1, x=2, x = 4, x=8 and so on. What is the potential at x = 0 due to this set of charges ?

172.

An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. The first part of mass 1 kg moves with a speed of 12 ms^{-1} and the second part of mass 2 kg moves with 8 ms^{-1} speed. If the third part flies off with 4 ms^{-1} speed, then its mass is

3 kg

5 kg

7 kg

17 kg

173.

A rod PQ of mass M and length L is hinged at end P. The rod is kept horizontal by a massless string tied to point Q as shown in figure. When string is cut, the initial angular acceleration of the rod is

$\frac{3\mathrm{g}}{2\mathrm{L}}$

$\frac{\mathrm{g}}{\mathrm{L}}$

$\frac{2\mathrm{g}}{\mathrm{L}}$

$\frac{2\mathrm{g}}{3\mathrm{L}}$

174.

A solid uniform sphere resting on a rough horizontal plane is given a horizontal impulse directed through its centre so that it starts sliding with an initial velocity v_{0}. When it finally starts rolling without slipping the speed of its centre is

$\frac{2}{7}{\mathrm{v}}_{0}$

$\frac{3}{7}{\mathrm{v}}_{0}$

$\frac{5}{7}{\mathrm{v}}_{0}$

$\frac{6}{7}{\mathrm{v}}_{0}$

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175.

Three identical square plates rotate about the axes shown in the figure in such a way that their kinetic energies are equal. Each of the rotation axes passes through the centre of the square. Then the ratio of angular speeds ω_{1} : ω_{2} : ω_{3} is

1 : 1 : 1

$\sqrt{2}:\sqrt{2}:1$

$1:\sqrt{2}:1$

$1:2:\sqrt{2}$

176.

A large number of particles are placed around the origin, each at a distance R from the origin. The distance of the centre of mass of the system from the origin is

equal to R

less than equal to R

greater than R

greater than equal to R

177.

Two particles A and B are moving as shown in the figure.

Their total angular momentum about the point O is

9.8 kg m

^{2}/ szero

52.7 kg m

^{2}/ s37.9 kg m

^{2}/ s

178.

A circular disc rolls on a horizontal floor without slipping and the centre of the disc moves with a uniform velocity v. Which of the following values of the velocity at a point on the rim of the disc can have ?

v

− v

2v

Zero

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